There is currently a great deal of interest in the light propagation characteristics of microstructured, or “holey,” optical fiber waveguides with novel cross-sections consisting of holes surrounded by glass. The holes may be empty or filled with a material chosen to influence the propagation. The ability to vary the transverse geometry due to advances in fabrication technology, combined with the large index contrasts possible with such structures, give multiple new degrees of freedom that potentially enable designs radically different than were previously possible with standard fibers.
Numerous interesting phenomena have already been observed in such waveguides. Among them are (i) guiding by the interference-based photonic band gap effect in fibers with an air core and a (truncated) transverse periodic lattice of air holes; (ii) variability of chromatic dispersion with microstructure; and resulting (iii) nonlinear effects in newly accessible spectral ranges due to microstructure-induced shifting zero dispersion point in glass core fibers.
Efficient and accurate mathematical modeling of light propagation characteristics of microstructured fiber is necessary for their design and analysis. A feature of most such structures is that they are inherently leaky due to the existence of paths leading from the core to the cladding that avoid the holes and pass only through the background glass. Such structures support no true guided modes, however, they may have leaky modes characterized by complex-valued propagation constants or effective indexes (scattering resonances); the leakage rate is given by the imaginary part.
Physically, this leakage is due to a combination of tunneling through the holes and propagating through the glass surrounding them. The ability to calculate such rates is clearly of fundamental importance. Other quantities of interest include the real parts of the effective indexes, which determine the response of the structure to longitudinal variations such as gratings, and the dispersion relations of the various leaky modes, which may be quite unusual compared to standard waveguides, due to the presence of large index contrasts and interference effects.
Many numerical studies of microstructure fibers have been undertaken based on direct numerical calculation of static Maxwell's equations in an effort to determine the system's modes. Some of these numerical studies are also able to capture the attenuation rates. A variety of methods have been used, among them: (1) the multiple expansion, which works well for structures with circular holes, (2) more general expansions in local bases and Fourier decompositions, which are applicable to more general geometries and (3) scalar and vector beam propagation, which are applicable to general geometries but have limitations in computing very small attenuation rates and have proven problematic in some more complex geometries.
All of these techniques have the characteristic that the computational difficulty of the calculations increases with the complexity of the structures. Accordingly, this creates a potentially intractable issue with today's proposed fiber structures.
Accordingly, new systems and methods are needed in the art for mathematically modeling complex photonic structures that are more accurate, flexible, computationally tractable and free of the constraints prior-art methods. Such new systems and methods will allow the propagation characteristics of the photonic structures to be analyzed in detail, leading to the discovery of new photonic structures having highly advantageous characteristics.